Controlling or syncing any F-Curve animation speed based on a path's Evaluation Time curve?
Ok, so I made some progress with this, but not exactly the way I wanted to.

I discovered that I can make an animation evaluation curve, similar to the path speed one, if I convert my animation to an Action (simply by switching to the NLA editor view), then selecting my animation strip, then activating the "Animated Strip Time" selection from the properties panel. Now, if you enter edit mode with 'tab' in the NLA and switch to the Graph editor view, an extra curve will be available for controlling Strip time. HOWEVER, there doesn't seem to be a way to control the values with a Driver (since the values are by default, like, keyframed and you can't remove the green and you can't have both keyframes and drivers at the same time on a property). A workaround is simply copying-pasting the Path Evaluation curve into the object animation Strip Time curve.

I will report back if I ever find a better way to do this.